An expression used to declare one's desire to have coitus with someone, coming from the verb 'Tap', which, in this context, is similar and related to screw, i.e. to put a thread on a piece of metal, or to insert said screw into a receptive orifice.
'That' replaces 'him' or 'her', suggesting the receiver of the screwing is just an object, to be sexually used and then cast aside.

"I'd SO tap that!" - By golly, I would very much like to slip my man-servant inside that fine filly!